Use tongs to char poblanos over a gas flame until blistered and black, 8 to 10 minutes. (Or preheat broiler to high and char peppers on a baking sheet.) Place peppers in a bowl and cover with plastic wrap; let steam 5 minutes. Slip skins off, halve peppers, discard seeds and chop.
In a large pot, heat oil over medium-high heat. Add peppers, onions, garlic, chili powder, oregano, cumin, 1 tsp salt and 1 tsp black pepper. Cook, stirring occasionally, until onions are golden brown and tender, 10 to 12 minutes.
Stir in tomato paste and chiles and cook, stirring continuously and scraping any caramelized spices off bottom of pot, until any excess moisture has evaporated, about 2 minutes.
Stir in broth, bring to a boil, then reduce heat to maintain a simmer. Add hominy, beans, and remaining salt and black pepper. Cook until heated through, about 30 minutes. Stir in lime juice. Season with salt and black pepper.
Serve topped with avocado, sour cream, pickled peppers and cilantro, with a squeeze of lime juice and some sea salt.